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 A216915 T(n, k) = Product{1<=j<=n, gcd(j,k)=1 | j} / lcm{1<=j<=n, gcd(j,k)=1 | j} for n >= 0, k >= 1, square array read by antidiagonals. 1

%I

%S 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,12,1,2,1,1,1,1,12,1,2,1,1,

%T 1,1,1,48,1,2,1,2,1,1,1,1,144,1,2,1,2,1,1,1,1,1,1440,3,8,1,12,1,2,1,1,

%U 1,1,1440,3,8,1,12,1,2,1,1,1,1,1,17280,3,80

%N T(n, k) = Product{1<=j<=n, gcd(j,k)=1 | j} / lcm{1<=j<=n, gcd(j,k)=1 | j} for n >= 0, k >= 1, square array read by antidiagonals.

%C T(n,k) = Product(R(n,k))/lcm(R(n,k)) where R(n,k) is the set of all integers up to n that are relatively prime to k.

%C T(n,k) = A216919(n,k)/A216917(n,k).

%F For n > 0:

%F A(n,1) = A025527(n);

%F A(4,n) = A000034(n);

%F A(n,n) = A128247(n).

%e k |n=0 1 2 3 4 5 6 7 8 9 10

%e ---+------------------------------------

%e 1 | 1 1 1 1 2 2 12 12 48 144 1440

%e 2 | 1 1 1 1 1 1 1 1 1 3 3

%e 3 | 1 1 1 1 2 2 2 2 8 8 80

%e 4 | 1 1 1 1 1 1 1 1 1 3 3

%e 5 | 1 1 1 1 2 2 12 12 48 144 144

%e 6 | 1 1 1 1 1 1 1 1 1 1 1

%e 7 | 1 1 1 1 2 2 12 12 48 144 1440

%e 8 | 1 1 1 1 1 1 1 1 1 3 3

%e 9 | 1 1 1 1 2 2 2 2 8 8 80

%e 10 | 1 1 1 1 1 1 1 1 1 3 3

%e 11 | 1 1 1 1 2 2 12 12 48 144 1440

%e 12 | 1 1 1 1 1 1 1 1 1 1 1

%e 13 | 1 1 1 1 2 2 12 12 48 144 1440

%o (Sage)

%o def A216915(n, k):

%o def R(n, k): return [j for j in (1..n) if gcd(j, k) == 1]

%o return mul(R(n,k))/lcm(R(n, k))

%o for k in (1..13): [A216915(n, k) for n in (0..10)]

%K nonn,tabl

%O 1,11

%A _Peter Luschny_, Oct 02 2012

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)